Hi Asineath,
Let's see what we can do to help with the Message app so you can start enjoying you new iPhone 13 Pro Max. A reason you may see this message, the feature Low Power Mode may be enabled.
Take a look at Use Low Power Mode to save battery life on your iPhone or iPad. It's a really good feature to use when your iPhone's battery starts to get low. But keeping it on can cause some features no work.
When Low Power Mode is on, your iPhone or iPad will last longer before you need to charge it, but some features might take longer to update or complete. Also, some tasks might not work until you turn off Low Power Mode, or until you charge your iPhone or iPad to 80% or higher.
You can also follow the steps here Restart your iPhone. A fresh restart can fix a lot of unusual behavior that pops up from time to time.
Either of these should help you with the Message app, and getting beyond the "uploading to iCloud paused" you are seeing. Reach back out if you have further questions.
Cheers!